Polarizers

Introduction

FRED has the capability to simulate polarization of rays through an optical system. Light sources can be randomly, circularly, or linearly polarized. Optical components that filter or manipulate polarization, such as birefringent wave plates and polarizers, can be accurately modeled. Some simple examples of polarization modeling in FRED can include absorptive dichroic and wiregrid polarizers, a calcite half-wave plate, and the Maltese cross phenomenon. Each of these features can be applied to more complex optical systems such as Liquid Crystal Displays (LCDs), interferometers, and polarization microscopes.

Polarizer Model

Consider a simple polarizer system, consisting of randomly-polarized rays followed by a dummy surface, an x-polarizer, and a detector surface. A coherent source is created with an elliptical grid plane of 10 x 10 rays traveling in the z-direction. The polarization state of the source is defined as “Polarized” & “Random” for (i) Ellipticity, (ii) Handedness, and (iii) Angle of Polarization Ellipse. The dummy and detector surface are elliptical planes with an “Absorb” coating and the “Halt All” Raytrace Control. Analysis Surfaces are assigned to each plane.

Figure 1. Randomly polarized light is filtered through an x-polarizer and collected by a detector.

There are two methods to model a polarizer. The simplest technique is to add a polarizer coating to a surface. In the Coatings category of the FRED document, the user can right-click and select Create a New Coating…. Under the drop-down menu, “Polarizer/Waveplate Coating (Jones Matrix)” can be selected. For this example, the “X Linear Polarizer” option is selected and assigned to the polarizer surface.

A more accurate technique is to model absorption-based polarization in a custom material. In the Material category of the FRED document, the user can right-click and select Create a New Material…. Under the drop-down menu, “Sampled Birefringent and/or Optically Active Material” can be selected. Here, the user defines different real refractive index values for each of the crystal axes, and may also define differing imaginary refractive index components. For this example, the crystal axis is oriented in the local +X direction (1,0,0).

An absorptive dichroic x-polarizer could be modeled with no=1.61, ne=1.65, ko=100, ke=0. A wiregrid x-polarizer can be modeled with no=1, ne=1.001, ko=100, ke=0. The imaginary refractive index indicates absorption. In this case, ordinary components of polarization (perpendicular to the crystal axis) are absorbed, leaving only polarization components along the +X crystal axis.

Polarization Spot Diagram

To monitor polarization of light through a system, an Analysis Surface can be used to produce a polarization spot diagram. After a raytrace is performed, the user can navigate to Analysis / Polarization Spot Diagram… The polarization of each ray with respect to the analysis surface will be symbolized as an ellipse with an arrow to designate handedness. If the z-axis of the analysis surface is aligned with the direction of ray propagation, handedness is determined by aligning your thumb in the direction that the ray is coming from and applying the right hand rule. For example, if a ray is propagating along the global +Z-axis and the analysis surface +Z axis is pointed in the same direction, align your thumb along the global -Z axis and apply the right hand rule to determine handedness of the ray.

As expected, rays coming from the light source have random polarization (Figure 2, left). After tracing rays through the x-polarizer to the detector, a new Polarization Spot Diagram can be generated to confirm that only x-polarized ray components propagate through the polarizer (Figure 3, right).

Figure 2. Polarization Spot Diagram. Left side: randomly-polarized light before entering the x-polarizer. Right side: x-polarized components of the rays pass through the polarizer and y-polarized components are absorbed by the polarizer. In the case of random incident polarization, ~50% of the incident power will be collected by the detector.